Va: maneuvering speed ad nauseam

After the reading the Va threads of my past questions, I found a
wonderful way to confuse myself. I notice that I've become quite good
at confusing myself and making things complicated. To give myself
some credit, I did search old messages but found no resolution. So
here we go...

I am sure most know the typical textbook definition of Va...goes
like..."the minimum speed at which the wing can produce lift equal to
the design load limit" or "the speed at which the pilot can use full
control deflections without over-stressing the airplane".

Essentially, it's the minimum airspeed that, coupled with a control
deflection to give you the critical angle of attack and CLmax, will
result in + 3.8 g's. Pulling any harder won't help since you'll stall
the airplane. Pulling with all your might as speeds below Va will
result in the airplane stalling without reaching the limit load factor
+ 3.8 g's. In essence, Va is the stall speed at the design load
factor of + 3.8 g's.

Now, the above seems to be what's commonly accepted.

Here's my question for this thread: Idealize the wing as a
cantilevered Euler beam representative of the wing spar ("the wing").
Assume the lift load to be a distributed elliptical spanwise,
transverse load, acting at the centroid of the section. Further
assume no other external loading such as drag loads.

The predominant stresses are bending (axial) stresses at the outer
regions of the spar caps and shear stresses in the spar web. Assume
that the failure mode is via the former.

Alright, so here, clearly, the failure of the wing is due to excessive
loading. The distributed load, expressed in X number of pounds per
inch, was too great. In fact, for the sake of simplicity, let's make
the distributed load a point load in pounds.

Now, we can say that the failure of the wing was due to excessive
FORCE which induced excessive stresses in the structure.

Consider that a certain airplane weighed at maximum takeoff weight is
designed to withstand + 3.8 g's (its design load). Actually,
airliners that I am familiar with are tested to ultimate load, or
1.5*design load (+ 5.7 g's before permanent deformation). For now,
we'll assume that at + 3.8 g, the plane's wings break off. That would
equal to a total force on both wings of 3.8 x 2550 lb or almost 10,000
lbs.

The thing that bothers me about Va is that it equates to a number of
g's ("design load") AND that Va is being rescaled for weight. By
doing so, Va becomes more of an acceleration criterion rather than a
structural criterion. It appears as though Va limits positive g
acceleration to + 3.8 g, not load itself.

In other words, Va adjusted for say, a lower weight, tells the pilot
"You will not exceed 3.8 g for your current weight, as you will stall
first". If the current weight was 2,000 lbs, the total load on the
wings would only equate to 7,600 lbs at + 3.8 g's, lower than the
design limit of 10,000 lbs of + 3.8 g's at max. takeoff weight. The
acceleration on the airplane would be a "limit load acceleration" but
would not produce a limit load condition, per se, structurally.

If Va was truly a structural consideration, it would not change
(regardless of weight), since no airspeed below Va coupled with any
non-stalled AOA, could produce limit loads of + 3.8 g as tested at max
takeoff weight of 2,550 lbs.

There may be severe flaws in my reasoning...please no flames and be
nice. It's a holiday.

Alex

The wing is not the only thing in the aircraft that might break.
Rework it assuming that the first thing to break is the engine mount
at 3.8g

(Koopas Ly) wrote in message om...

....Consider that a certain airplane weighed at maximum takeoff weight is
designed to withstand + 3.8 g's (its design load). Actually,
airliners that I am familiar with are tested to ultimate load, or
1.5*design load (+ 5.7 g's before permanent deformation). For now,
we'll assume that at + 3.8 g, the plane's wings break off. That would
equal to a total force on both wings of 3.8 x 2550 lb or almost 10,000
lbs.

The thing that bothers me about Va is that it equates to a number of
g's ("design load") AND that Va is being rescaled for weight. By
doing so, Va becomes more of an acceleration criterion rather than a
structural criterion. It appears as though Va limits positive g
acceleration to + 3.8 g, not load itself.

In other words, Va adjusted for say, a lower weight, tells the pilot
"You will not exceed 3.8 g for your current weight, as you will stall
first". If the current weight was 2,000 lbs, the total load on the
wings would only equate to 7,600 lbs at + 3.8 g's, lower than the
design limit of 10,000 lbs of + 3.8 g's at max. takeoff weight. The
acceleration on the airplane would be a "limit load acceleration" but
would not produce a limit load condition, per se, structurally.

If Va was truly a structural consideration, it would not change
(regardless of weight), since no airspeed below Va coupled with any
non-stalled AOA, could produce limit loads of + 3.8 g as tested at max
takeoff weight of 2,550 lbs.

There may be severe flaws in my reasoning...please no flames and be
nice. It's a holiday.

Alex

Not a dumb question, and many have misunderstood Va. I'm no
expert either, but as I understand it, the 3.8 G limit is predicated
on gross weight, or as you point out for your particular airplane,
almost 10,000 lbs.
Flying at less than gross, the airplane will be less likely to
stall as say, full up elevator is abrubtly applied, and will tend to
climb. Climbing reduces the angle of attack, preventing the stall and
maintaining the load on the wing, and the same 10,000 lbs of force
could be achieved easily. It would be higher than 3.8 G, but as I
said, the G load factor is based on gross weight.
So for less than gross weights, Va must be reduced by the square
of the decrease in weight. As Kirschner calculates it, a 20% weight
reduction should give a 10% Va reduction, and a 40% weight reduction
should give a Va 20% lower.
Don't forget that the wing is not the only structure in the
airplane. Several aircraft have been know to fail the tail first;
airplanes like the 210 and Bonanza, which are slippery and build speed
rapidly in the typical spiral entered after the non-instrument pilot
enters cloud. Upon popping out of the overcast at 400 feet, with the
ground coming up fast, he pulls back hard and the stab fails downward,
the airplane pitches forward over onto its back, and the wings fail
downward. End of story.

Dan

Andrew Rowley wrote in message . ..
The wing is not the only thing in the aircraft that might break.
Rework it assuming that the first thing to break is the engine mount
at 3.8g

Andrew,

I think I understand now. Let me see if I get it...

To rework the analysis, I'll assume that the weight of the airplane is
mainly supported by the wings, and that other components such as the
engine mount are essentially invariant in static 1g weight. In other
words, by overloading the airplane with other bodies, ballast, and
such, the weight of the engine mount does not change. If that is so,
I can see how such *individual* components may be "g limited" with
respect to their own inertia. Does this follow your reasoning?

Thanks,
Alex

(Koopas Ly) wrote:

I think I understand now. Let me see if I get it...

To rework the analysis, I'll assume that the weight of the airplane is
mainly supported by the wings, and that other components such as the
engine mount are essentially invariant in static 1g weight. In other
words, by overloading the airplane with other bodies, ballast, and
such, the weight of the engine mount does not change. If that is so,
I can see how such *individual* components may be "g limited" with
respect to their own inertia. Does this follow your reasoning?

almost... the engine mount needs to support the weight of the engine
multiplied by the number of Gs. so if the engine weighs 100kg at 3.8G
the mount is supporting 380kg. At 5G it has to support 500kg. So force
on the wings at high Gs may go down as your total weight goes down,
but the force on other items (engine mount, baggage floor, basically
any part of the airframe that has to support something) does not.

Andrew Rowley wrote in message . ..
(Koopas Ly) wrote:

I think I understand now. Let me see if I get it...

To rework the analysis, I'll assume that the weight of the airplane is
mainly supported by the wings, and that other components such as the
engine mount are essentially invariant in static 1g weight. In other
words, by overloading the airplane with other bodies, ballast, and
such, the weight of the engine mount does not change. If that is so,
I can see how such *individual* components may be "g limited" with
respect to their own inertia. Does this follow your reasoning?

almost... the engine mount needs to support the weight of the engine
multiplied by the number of Gs. so if the engine weighs 100kg at 3.8G
the mount is supporting 380kg. At 5G it has to support 500kg. So force
on the wings at high Gs may go down as your total weight goes down,
but the force on other items (engine mount, baggage floor, basically
any part of the airframe that has to support something) does not.

The engine mount on most light aircraft is designed to withstand 9
G's minimum. And as I said earlier, the 3.8 figure is based on gross
weight. Reducing gross would allow them to take a higher G figure but
the same net force.
Cessna also states in the 172 POH that it's designed to 150% of
the G figures given, or 5.7 G's. I think the 3.8 figure would be the
yield point, where things begin to bend, and the 150% figure would
break them entirely. Or something like that.

Dan

The engine mount on most light aircraft is designed to withstand 9
G's minimum.

Where do you get this figure?

(Dan Thomas) wrote
Cessna also states in the 172 POH that it's designed to 150% of
the G figures given, or 5.7 G's. I think the 3.8 figure would be
the yield point, where things begin to bend, and the 150% figure
would break them entirely. Or something like that.

The C-172 is probably wing limited, since at 200-300 under maximum
gross weight, it falls in the Utility Category with +4.4g allowed
for the limit load and +6.6g for the ultimate load.

Bob Moore

(Dan Thomas) wrote:

The engine mount on most light aircraft is designed to withstand 9
G's minimum. And as I said earlier, the 3.8 figure is based on gross
weight. Reducing gross would allow them to take a higher G figure but
the same net force.
Cessna also states in the 172 POH that it's designed to 150% of
the G figures given, or 5.7 G's. I think the 3.8 figure would be the
yield point, where things begin to bend, and the 150% figure would
break them entirely. Or something like that.

One of the earlier posts assumed for the purposes of calculation that
the wings break when exceeding 3.8g at gross weight. I was merely
continuing that assumption. All I was trying to illustrate was that
there are some parts of the airframe where the loads are not
aerodynamic and where the loads do not reduce with reduced aircraft
weight - which is why Va reduces with reduced weight.

Andrew Rowley wrote in message . ..
(Koopas Ly) wrote:

I think I understand now. Let me see if I get it...

To rework the analysis, I'll assume that the weight of the airplane is
mainly supported by the wings, and that other components such as the
engine mount are essentially invariant in static 1g weight. In other
words, by overloading the airplane with other bodies, ballast, and
such, the weight of the engine mount does not change. If that is so,
I can see how such *individual* components may be "g limited" with
respect to their own inertia. Does this follow your reasoning?

almost... the engine mount needs to support the weight of the engine
multiplied by the number of Gs. so if the engine weighs 100kg at 3.8G
the mount is supporting 380kg. At 5G it has to support 500kg. So force
on the wings at high Gs may go down as your total weight goes down,
but the force on other items (engine mount, baggage floor, basically
any part of the airframe that has to support something) does not.

Thanks for the clarification.

What is the critical "item" that will break at 3.8 g's on a light GA
airplane like a C172? Is it the engine mount? I see that's it's
often mentioned as the "weakest link".

It's my opinion that the definition of Va taught to private pilots
leads to a false understanding that the wings will break at 3.8 g's.
The nuance we've discussed is not stressed. Why? I don't know.

Best regards,
Alex